On May 6, 2009, at 1:13 PM, Paolo Bardella wrote:
Is it possible to use MPB in order to study a 2D or 3D structure
whose refractive index n(x,y,z) is periodic only in one direction
n(x,y,z)=n(x,y,z+L) ?
MPB always imposes periodic boundary conditions.
However, in certain circumstances one can use it to study non-periodic
structures, as long as the desired solutions are localized in the non-
periodic directions, in which case one can use a supercell technique.
For example, to study a photonic-crystal slab, which is periodic in
two directions (xy) but non-periodic in the third (z), you can still
use MPB if the modes of interest are the guided modes in the slab.
These modes are exponentially decaying in the z direction away from
the slab, so as long as the computational cell is big enough in the z
direction the boundary conditions in the z direction have an
exponentially small effect on the solutions.
Steven
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